Beautifying freeform drawings using arc and circle center snapping

ABSTRACT

Embodiments of the present invention are directed to beautifying freeform input paths in accordance with paths existing in the drawing (i.e., resolved paths). In some embodiments of the present invention, freeform input paths of a curved format can be modified or replaced to more precisely illustrate a path desired by a user. As such, a user can provide a freeform input path that resembles a path of interest by the user, but is not as precise as desired. Based on existing paths in the electronic drawing, a path suggestion(s) can be generated to rectify, modify, or replace the input path with a more precise path. In some cases, a user can then select a desired path suggestion, and the selected path then replaces the initially provided freeform input path.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/962,269, filed Apr. 25, 2018 and titled “BEAUTIFYING FREEFORMDRAWINGS USING TRANSFORMATION ADJUSTMENTS,” which is itself a divisionalof U.S. patent application Ser. No. 15/138,037 (now issued as U.S. Pat.No. 9,984,481), filed Apr. 25, 2016, and entitled “BEAUTIFYING FREEFORMDRAWINGS,” the entirety of each of the aforementioned applications areincorporated by reference herein.

BACKGROUND

Freeform drawings provide a simple way for users to create content tographically represent an image, idea or principle. Freeform drawings arealso referred to as electronic sketches, and are generally unconstrainedinputs that are specified using freeform paths to mimic a user's abilityto draw on a piece of paper using a pen or pencil. In computing devices,a user may define freeform paths that are detected using touchscreenfunctionality of a display device (e.g., as a gesture, through use of astylus), using a cursor control device, and so on.

Although a user may quickly input freeform paths to compose a drawing,the freeform paths are typically informal and thus not intended as afinished work. Conventional techniques have been developed to increaseprecision and the look-and-feel of these freeform drawings. Theseconventional techniques, however, typically require detailed knowledgeon the part of a user and involve a significant amount of time toperform.

SUMMARY

Aspects of the present disclosure relate to beautifying freeform inputpaths in accordance with paths existing in the drawing (i.e., resolvedpaths). In this regard, freeform input paths of a curved format can bemodified or replaced to more precisely illustrate a path desired by auser. As such, a user can provide a freeform input path that resembles apath of interest by the user, but is not as precise as desired. Based onexisting paths in the electronic drawing, a path suggestion(s) can begenerated to rectify, modify, or replace the input path with a moreprecise path. In some cases, a user can then select a desired pathsuggestion, and the selected path then replaces the initially providedfreeform input path.

To generate path suggestions for curved input paths, embodiments of thepresent invention describe various analytics and rules that can beapplied to beautify a curved input path. In particular, upon obtainingan input path, the input path can be analyzed in accordance with one ormore resolved paths (paths previously existing in the drawing) togenerate path suggestions. Examples of such rules that provide pathsuggestions for curved input paths include arc and circle centersnapping, path transformation, and transformation adjustment. Further,to enhance path suggestions for curved input paths, in someimplementations, a curved input path can be divided into segments basedon detected corners within the curved input path. Each segment can thenbe assessed using beautification rules in light of prior assessedsegments and/or resolved paths to generate path suggestions associatedwith that particular segment and/or the entire curved input path.

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used as an aid in determining the scope of the claimed subjectmatter.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is described in detail below with reference to theattached drawing figures, wherein:

FIG. 1 is an illustration of an environment in an example implementationthat is operable to employ freeform drawing beautification techniquesdescribed herein;

FIG. 2 depicts an example of a beautification workflow of abeautification assistant component, in accordance with embodiments ofthe present invention;

FIG. 3 depicts an implementation of a beautification assistantcomponent, in accordance with embodiments of the present invention;

FIG. 4 depicts an example of reduction of memory and computationcomplexity using path sampling, according to embodiments of the presentinvention;

FIG. 5 illustrates examples of beautification rules, in accordance withembodiments of the present disclosure;

FIG. 6 illustrates examples of beautification rules, in accordance withembodiments of the present invention;

FIGS. 7A-7B illustrates an example of step-transform snapping, inaccordance with embodiments of the present disclosure;

FIGS. 8A-8C illustrate an example of arc and circle center snapping inaccordance with embodiments of the present disclosure;

FIG. 9 illustrates an example of multi-segment path processing accordingto embodiments of the present disclosure;

FIGS. 10A-10C illustrate visual annotations of applied rules, inaccordance with embodiments of the present disclosure;

FIG. 11 is a flow diagram showing a first method for facilitatingbeautification of freeform drawings in accordance with embodiments ofthe present disclosure; and

FIG. 12 is a flow diagram showing a second method for facilitatingbeautification of freeform drawings in accordance with embodiments ofthe present disclosure;

FIG. 13 is a flow diagram showing a third method for facilitatingbeautification of freeform drawings in accordance with embodiments ofthe present disclosure;

FIG. 14 is a flow diagram showing a fourth method for facilitatingbeautification of freeform drawings in accordance with embodiments ofthe present disclosure; and

FIG. 15 is a block diagram of an exemplary computing environmentsuitable for use in implementations of the present disclosure.

DETAILED DESCRIPTION

The subject matter of the present invention is described withspecificity herein to meet statutory requirements. However, thedescription itself is not intended to limit the scope of this patent.Rather, the inventor has contemplated that the claimed subject mattermight also be embodied in other ways, to include different steps orcombinations of steps similar to the ones described in this document, inconjunction with other present or future technologies. Moreover,although the terms “step” and/or “block” may be used herein to connotedifferent elements of methods employed, the terms should not beinterpreted as implying any particular order among or between varioussteps herein disclosed unless and except when the order of individualsteps is explicitly described.

Freeform drawings, such as electronic sketches, are one of the simplestways to visualize ideas. One key advantage is that the user is notrequired to have specialized knowledge of particular drawing softwarenor any advanced drawing skills. In practice, however, these skills maybecome necessary to improve the visual fidelity of the resultingdrawing. Conventional techniques used to make the freeform input lookmore precise and polish generally require the user to have experiencewith drawing software. Even if the user has this experience, use ofconventional drawing software could take even longer to perform thanmaking the freeform input itself.

Further, many of such conventional techniques visually improve onlystraight line segments and utilize a set of basic rules to make suchfreeform input look more precise. Users, however, typically providefreeform input in the form of straight line segments as well as curvedsegments. As with making straight line freeform input look more precise,users often desire input strokes in the form of arbitrarily curved pathsto also look more precise. Although some conventional implementationscan recognize a curve, other existing paths are not taken intoconsideration to visually improve curve segments such that the curvedsegments appear more precise. Contemplation of other existing paths inassociation with an input path can enable a more interactive design forthe user and provide a more precise curved path in the drawing.

Accordingly, embodiments of the present invention are directed tobeautifying curved input paths in accordance with paths existing in thedrawing (i.e., resolved paths). In particular, input paths of a curvedformat can be modified or replaced to more precisely illustrate a pathdesired by a user. As such, a user can provide a freeform input paththat resembles a path of interest by the user, but is not as precise asdesired. Based on existing paths in the electronic drawing, however, oneor more path suggestions can be provided to rectify, modify, or replacethe input path with a more precise path.

To generate path suggestions for curved input paths, embodiments of thepresent invention describe various analytics and rules that can beapplied to beautify a curved input path. In particular, upon obtainingan input path, the input path can be analyzed in accordance with one ormore resolved paths (paths previously existing in the drawing) togenerate path suggestions.

One example used to beautify an input path is an arc and circle centersnapping rule. An arc and circle center snapping rule is generally usedto align a center point of an input arc or circle with a point of aresolved path. For example, a center point associated with an arc orcircle might be aligned with an endpoint of another path, a centerassociated with another arc or circle path, a center of rotationassociated with another path, a center of a polygon associated with aresolved path (e.g., polygons composed from series of line segments),etc. To align a center point of an arc or circle with a resolved pathpoint, an adaptive distance between an input center and potentialresolved path points can be evaluated. When the input center point iswithin an adaptive distance of a resolved path point, the input centerpoint might be snapped or aligned with the resolved path point and theradius of the arc or circle can be adjusted. Such an adaptive searchradius can be beneficial to effectively capture a user's intent. Forexample, arcs with small angular spans are difficult to draw preciselywithout a guide (e.g., users tend to draw the arc too curved). As such,the identified center of the input arc might be positioned at a distancetoo far apart from a desired center point. As such, adaptive expansionof the search radius increases the likelihood that an imprecise inputwill provide the user the expected, precise output.

Other examples used to beautify an input path include a pathtransformation rule and a transformation adjustment rule. A pathtransformation rule is generally used to generate a path suggestion(s)that is a transformation of a resolved path that is sufficiently similarto an input path. As such, upon detecting that an input path issufficiently similar to a resolved path, for example, using an affinesimilarity transformation matrix, the resolved path can be transformed(e.g., using the affine similarity transformation matrix) and providedas a path suggestion.

Further, as can be appreciated, in some cases, the transformed resolvedpath can be adjusted to result in a more precise path suggestion. Forexample, assume that a transformed resolved path has a rotation of 43degrees. In such a case, as the user may have desired to rotate the path45 degrees, an adjusted transformation can be applied such that the pathsuggestion is rotated 45 degrees. At a high-level, and as described inmore detail below, to determine an adjusted transformation, thetransformed resolved path can be separated into components, such as arotation, scale, and translation component. The various components canbe compared to target components and, if within a threshold ofsimilarity, the component value can be adjusted to the target componentvalue. For instance, when the rotation component of a transformedresolved path is 43 degrees and a target component value is 45 degrees,upon determining that 43 degrees is sufficiently similar to 45 degrees,a path suggestion can be provided with a 45 degree transformation.

In some implementations, beautifying curved input paths in accordancewith paths existing in the drawing (i.e., resolved paths) is performedusing multi-segment path processing. Multi-segment path processingenables a single input path to be divided into segments that areseparately analyzed in light of prior assessed segments and/or resolvedpaths. In particular, a curved input path can be segmented based ondetection of corners within the curved input path. The segments can thenbe processed sequentially to generate one or more path suggestions usingbeautification rules (e.g., arc and circle center snapping rule, pathtransformation rule, a transformation adjustment rule, etc.) in light ofpreviously analyzed segments and/or resolved paths. In some cases, toreduce the number of path suggestions, the number of path suggestionscan be limited for each processed segment.

Although aspects of the present invention are generally described hereinin relation to curved input paths, as can be appreciate, this technologycan be implemented in relation to other input paths. The above conceptsand others, including variations and combinations thereof, arecontemplated as being within the scope of the present disclosure.

Turning now to FIG. 1, a block diagram is provided showing an example ofan operating environment in which some implementations of the presentdisclosure may be employed. It should be understood that this and otherarrangements described herein are set forth only as examples. Otherarrangements and elements (e.g., machines, interfaces, functions,orders, and groupings of functions, etc.) can be used in addition to orinstead of those shown, and some elements may be omitted altogether forthe sake of clarity. Further, many of the elements described herein arefunctional entities that may be implemented as discrete or distributedcomponents or in conjunction with other components, and in any suitablecombination and location. Various functions described herein as beingperformed by one or more entities may be carried out by hardware,firmware, and/or software. For instance, some functions may be carriedout by a processor executing instructions stored in memory.

FIG. 1 is an illustration of an environment 100 in an exampleimplementation that is operable to employ freeform drawingbeautification techniques described herein. The illustrated environment100 includes computing device 102 having a display device 104 on which auser interface may be displayed to support user interaction. Thecomputing device 102 may be configured in a variety of ways. Thecomputing device 102, for instance, may be configured as a desktopcomputer, a laptop computer, a mobile device (e.g., assuming a handheldconfiguration such as a tablet or mobile phone as illustrated), and soforth. Thus, the computing device 102 may range from full resourcedevices with substantial memory and processor resources (e.g., personalcomputers, game consoles) to a low-resource device with limited memoryand/or processing resources (e.g., mobile devices). Additionally,although a single computing device 102 is shown, the computing device102 may be representative of a plurality of different devices, such asmultiple servers utilized by a business to perform operations “over thecloud.”

The computing device 102 is illustrated as including a freeform drawingcomponent 106. The freeform drawing component 106 is representative offunctionality of the computer device 102 to accept and process userinputs to form freeform drawings for display by the display device 104.A user, for example, may provide inputs using a cursor control device,gesture, stylus, and so on to define a freeform drawing for output. Thefreeform drawing component 106 is also illustrated as including abeautification assistant component 108 that is representative offunctionality to rectify a freeform drawing input by a user in a mannerthat maintains simplicity and speed of freeform sketching while stilltaking into account geometric relations.

At a high level, beautification assistant component 108 rectifies afreeform drawing input by a user, such as input 112. Based on the userinput 112, suggested drawings 114, 116, and 118 can be generated andprovided to the user. Assume that the user desires the original freeforminput to transform to suggested drawing 116. In such a case, the usercan select suggested drawing 116 to replace the original freeform inputwith the suggested drawing 116.

FIG. 2 depicts an example 200 of a beautification workflow of thebeautification assistant component 108 of FIG. 1. Incrementalbeautification performed by the beautification assistant component 108is shown as successive input lines 202-214 and adjusted lines 204′-214′through stages 1-7 to arrive at a beautification result 216, ascontrasted with drawn collection 218 of input lines 202-214.

For example, a user initially draws input line 202, which remains as isbecause there are no other lines that serve as a basis for adjustment.Input line 204 is then drawn, which is adjusted by the beautificationassistance component 108 to form adjusted line 204′ to form a mirrorimage of the input line 202 through a process referred to as reflection.Input line 206 is then drawn by a user, which is then adjusted by thebeautification assistant component 108 to have a symmetric curve asshown for adjusted line 206′ through arc fitting. Similarly, input line208 is drawn by a user and adjusted by the beautification assistantcomponent 108 to have a symmetric curve as shown for adjusted line 208′.

An input line 210 is then drawn to represent a plant leaf, which issufficiently different from other lines and, as such, is not adjusted.Curve identity, reflection, and scaling are then used to adjustsubsequent input lines 212, 214 to form adjusted lines 212′, 214′ thatare based at least in part on adjusted line 210′ and, as such, mimiccharacteristics of the plant leaf. Thus, as the freeform drawingcontinues, more suitable geometric constraints emerge and are applied bythe beautification assistant component 108 as suggestions, such as curveidentity (e.g., stages 2, 6, 7), reflection (e.g., stages 2 and 6), andarc fitting (stages 3, 4). Thus, as is readily apparent throughcomparison with the input 218 and final output freeform art at theresult 216, the beautification assistant component 108 supportsefficient freeform drawing with results that are ready for sharing withothers.

FIG. 3 depicts an implementation of a beautification assistant componentused to facilitate beautifying curved input paths in accordance withpaths existing in the drawing (i.e., resolved paths). As shown in FIG.3, the beautification assistant component 302 can include a pathanalyzer 304, a path suggestion generator 306, and a path provider 308.As shown in FIG. 3, the input to the beautification assistant component302 includes an input path 312 and a set of one or more existingresolved paths 314. An input path refers to a path or stroke that iscurrently or most recently provided by a user (e.g., via contact with atouch display, a mouse, etc.). An input path may be of any shape orsize. For instance, as described herein, an input path may be a linesegment or path, or a curved segment or path. A curved segment or pathgenerally refers to any path with a curve, such as an arc, a circle, aspiral, a general cubic Bezier curve, or any type of curve path. In thisregard, a curved path gradually deviates from being straight for some orall of its length. A resolved path refers to a path previously input bya user (prior to an input path). A resolved path is generallyestablished as an aspect of the drawing, or a path that has become fixedin the drawing. For example, a resolved path may be a previouslyprovided freestyle path or a previously provided freestyle path that hasbeen converted to or replaced with a beautified or modified path.

Paths or strokes, such as input path 312, can be input in any number ofmanners. For instance, in some implementations, a user may use a touchinput to provide a path or stroke to the computing device. In otherimplementations, a user might use a mouse, a digital pen, or othercomponent to input freeform paths to the computing device.

Input path 312 and resolved path(s) 314 can be received, retrieved,referenced, or otherwise accessed at any time. For example, inaccordance with recognizing that a user has completed an input path,such as input path 312, data associated with the input path (input pathdata) and a group of resolved paths (resolved path data) can beobtained. In some cases, data for each of the resolved paths associatedwith the drawing might be obtained. In other cases, data for aparticular set of the resolved paths associated with the drawing mightbe obtained. For instance, resolved paths positioned near or proximateto the input path might be referenced, resolved paths input at a timenear or proximate to the time of the input path might be referenced,etc.

Upon obtaining path data, such as input path data and resolved pathdata, the path analyzer 304 can utilize path data to analyze input pathsand/or resolved paths. Path data generally refers to any data indicatinga path or stroke associated with an input path or a resolved path. Forinstance, path data may represent position or placement of a curved pathon a drawing canvas. As another example, path data may represent asequence of cubic Bezier curves. Although analysis of path data isgenerally described herein with reference to input paths and resolvedpaths, as can be appreciated, in some cases, the resolved paths may havebeen previously analyzed and such analysis data stored in a data storefor reference. Using analysis from previously resolved and analyzedpaths can reduce computation performed by a computing device.

In some implementations, the path analyzer 304 can analyze paths byperforming corner detection, path sampling, and/or path matching. Cornerdetection, path sampling, and/or path matching may be performed toanalyze paths (e.g., input paths) such that one or more path suggestionscan be generated. As can be appreciated, in implementation, the pathanalyzer 304 may only perform a portion or none of corner detection,path sampling, and/or path matching, or may perform other or additionalanalyses of paths. For instance, depending on a particularimplementation, or a particular input stroke, only path sampling andpath matching may be performed.

Corner detection generally refers to analysis of a path (e.g., afreeform input path) to detect one or more corners in the path. Cornerdetection can be performed so that a path with multiple segments (e.g.,parts of an unprocessed user input) can be processed as a whole and/orindividually. In this regard, an entire input path with multiplesegments, defined or split by corner features, can be analyzed toprovide a path suggestion(s). Alternatively or additionally, segmentsdefined or split by corner features of an input path can be individuallyprocessed to provide suggestion paths. By way of example, assume that asingle input stroke is drawn generally in the shape of a triangle. Forinstance, a user may draw a triangle by way of touch input withoutlifting her or his finger from the touch screen until the triangle iscompleted, or mostly completed. In such a case, corners of the trianglecan be detected to generate multiple segments for processing orevaluating. As such, once divided into segments, the path suggestiongenerator 306 can utilize the segments using one or more rules togenerate path suggestions for the input path, as described in moredetail below.

Corner detection can be applied in any manner. By way of example only,an input path drawn by a user (e.g., converted to a sequence of cubicBezier curves) can be assessed to identify curves in the path.Identified curves can be sampled to generate sample points along thepath. For example, in one implementation, a curve can be sampled with asmall step size (e.g., 2 view-space pixels). In accordance withidentifying sample points, a tangent vector may be calculated at eachsample point, e.g., along the curve. Using successive samples, anangular turn can be calculated. For instance, using a sliding window ofthree successive samples, an angular turn value can be calculated ateach sample position except the first and last sample point. Thegreatest angular turn value among the sample points of the curve may beidentified or designated as a point at which to break or segment theoriginal input sequence. Such a method can be performed at any number ofidentified curves (e.g., each identified curve) to generate any numberof segments from a single input path. In some cases, to remove outliers,such as unwanted “hooks” at the end(s) of the input path, a segmenthaving a length that is small in comparison to the rest of the segmentscan be discarded. By way of example only, a segment having a length thatis less than 15% of the length-wise closest other segment can bediscarded.

Path sampling generally refers to identifying points on a path as samplepoints for use in analyzing the path. As can be appreciated, analyzingcubic Bezier curves may be difficult. As such, in some implementations,operations may be performed on sampled paths, that is, paths of samplepoints. Path sampling may be performed for input paths and resolvedpaths. As can be appreciated, as resolved paths are established, in somecases, path sampling for resolved paths can be precomputed and stored.

Further, in some cases, to reduce the memory requirement andcomputational complexity of different path comparisons, path samplingcan be simplified, for instance, using the Ramer-Douglas-Peuckeralgorithm. To this end, for a polyline p, the Ramer-Douglas-Peuckeralgorithm can identify a reduced version (path sample) p′ with fewerpoints within a given tolerance ϵ, that is, points of p′ lie within thedistance ϵ (e.g., ϵ=4 view-space pixels) of the original input path. Byway of example, and with reference to FIG. 4, an original Bezier path402 is equidistantly sampled, giving a polyline 404. TheRamer-Douglas-Peucker algorithm then recursively simplifies the polylineby omitting points closer than “ϵ” to the current approximation as shownat example 406, finally constructing a simplified polyline 408. In anexample implementation, “ϵ=4” view-space pixels at the time the path wasdrawn is used for path sampling. View-space pixels may be used to resultin distance measurements that are magnification independent.

Path matching refers to determining or identifying whether one pathmatches another. In particular, a determination can be made as towhether an input path matches or corresponds with a resolved path. Apath may match or correspond with another path if the paths aregenerally classified as the same shape or are different instances of thesame template. For example, a path can be identified as matching if itis the same shape, but a different size, or rotated.

At a high-level, to detect that two paths match, paths can be alignedand, thereafter, evaluated for similarity between the two paths. Toalign paths, affine similarity transform can be used. Affine similaritytransfer refers to a composition of a rotation, scale, and/ortranslation. Generally, with affine similarity transfer, the shape isnot changed or skewed. To align paths, an affine similarity matrix thattransforms one path (e.g., resolved path) to another path (e.g., aninput path) as closely as possible can be identified or determined. Anaffine similarity matrix M may be represented as follows:

$\quad\begin{bmatrix}{s\;\cos} & {{- s}\;\sin} & 0 \\{s\;\sin} & {s\;\cos} & 0 \\{tx} & {ty} & 1\end{bmatrix}$

wherein s cos=s*cos θ, s sin=s*sin θ, θ represents the rotation angle, srepresents the scale, and (tx, ty) represents the translation.

In some cases, to compute an affine similarity transformation matrix Mthat transforms one path to another, two equal length lists of points,each including N equally-spaced samples (e.g., 10 points) from theresolved path and the input path, can be used. For instance, assume that{P_(i)} are the points from the resolved path, and {Q_(i)} are thepoints from the input path, the matrix M that minimizes the sum ofsquared distances E can be determined as follows:E=Σ _(i=1) ^(N) ∥P _(i) *M−Q _(i)∥²  Equation 1

Such a quadratic function of variables s cos, s sin, tx, and ty can besolved as a least-squares problem over such variables. In particular,this enables selection of a matrix M so that the matrix M multiplied bythe resolved path P results in the best match to the input path Q.

As can be appreciated, an affine similarity transformation matrix M canbe identified for any number of input-resolved path pairs. For example,an affine similarity transformation matrix M might be determined foreach resolved path with respect to an input path. To this end, if fiveresolved paths exist, five similarity transformation matrices may bedetermined, one for each of the resolved paths paired with the inputpath. As another example, an affine similarity transformation matrix Mmight be determined for a specific set of resolved paths with respect toan input path (e.g., resolved paths positioned near the input path,etc.).

As described, upon aligning paths, a similarity between paths can bedetermined. To determine similarity between paths, such as an input pathand a resolved path, Fréchet distance, or a variant thereof, can beused. Fréchet distance is generally described as a measure of similaritybetween curves, which can take into account the location and ordering ofpoints along the curves. Assume that (M,d) denotes a metric space andthe path is defined as a continuous mapping f: [a, b]→M, where a, b∈

≤b. Given two paths f: [a, b]→M and g: [a′,b′]→M, Fréchet distance δ_(F)is generally defined as:

$\begin{matrix}{{\delta_{F}( {f,g} )} = {\inf\limits_{\alpha,\beta}\;{\max\limits_{t\;{\epsilon{\lbrack{0,1}\rbrack}}}\;{d( {{f( {\alpha(t)} )},{g( {\beta(t)} )}} )}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

wherein α(resp. β) is an arbitrary continuous non-decreasing functionfrom [0,1] onto [a, b](resp. [a′,b′]. In some cases, before computingthe Fréchet distance, the resolved path samples can be multiplied by thecorresponding affine similarity transformation matrix M. A Fréchetdistance can be calculated in association with each similaritytransformation matrix M For instance, assume that a similaritytransformation matrix M is determined for each input-resolved path pair.In such a case, a Fréchet distance, or measure of similarity, can bedetermined for each input-resolved path pair. The measures of similaritycan then be compared to one another, or measured against a threshold, todetermine one or more resolved paths to which the input path is similar.

As will be described, analysis associated with corner detection, pathsampling, and/or path matching can be used by the path suggestiongenerator 306 to generate path suggestions. A path suggestion refers toa suggestion or recommendation of a path that can replace or modifyanother path, such as an input path. In some cases, a path suggestion(s)can be provided as an alternative or option for an input path that ispresented to a user for selection. Upon the user selecting a particularpath suggestion, a corresponding path, such as an input path, can bereplaced or modified to replicate the selected path suggestion. In othercases, a path suggestion(s) may be automatically implemented to modifyor replace an input path. For example, an input path may beautomatically converted from one curved line to another curved linewithout selection from a user. As can be appreciated, in such cases, theuser may have the option to undo the automatic implementation.

Path suggestions can be identified or generated using any number ofbeautification rules. Beautification rules generally refer to rules oralgorithms used to generate a suggestion for a path that might beautify,or make more precise, the path (e.g., input path). Any number ofbeautification rules can be accessed and used to generate pathsuggestions. In some cases, each rule might be applied to determine anyappropriate path suggestions. In other cases, a portion of rules mightbe applied to determine any appropriate path suggestions. For example,assume a path is a curved path. In such a case, beautification rulesassociated with curved paths may be accessed and used to determine anypath suggestions to generate and/or provide to a user. Beautificationrules can be accessed from a rule data store.

FIG. 5 shows examples of beautification rules that are supported by thebeautification assistant component 302 to perform beautification.Example rules, some of which are provided in more detail below, includeendpoint snapping, end-tangent alignment, line parallelism, lineperpendicularity, line length equality, arc-center snapping, pathoffset, path transformation, and step transformation. In some cases, thepath suggestion generator 306 can treat these rules as an extensible setof self-contained rules, each built as a black box and independent ofother rules. Each of the rules can represent a single geometricproperty, such as having an endpoint snapped or as being a reflectedversion of an existing path.

Although input provided to each rule may differ, such input may includean input path, such as an end-to-end-connected series of Bezier curves,and a set of existing resolved paths. Input may additionally oralternatively include data provided from the path analyzer component304. For example, an indication of detected corners, an indication ofpath samples, and/or an indication of path matches (e.g., resolved pathsthat match or are similar to an input path), etc. The particular inputprovided to and/or utilized by the path suggestion generator 306 maydepend on the beautification rule(s) being assessed. Generally, the pathsuggestion generator 306 evaluates the likelihood that an input pathconforms to a geometric property considering one or more resolved paths.

One beautification rule that can be applied to generate a pathsuggestion(s) for an input path is a path transformation rule. Pathtransformation refers to transforming a resolved path, by rotating,scaling, and/or translating, such that the transformed path generallyaligns with an input path. A transformation that generally orsubstantially aligns a resolved path within to the input path can beidentified. A resolved path might be generally or substantially alignedwith an input path when the paths are within a predetermined thresholddistance, a range, or an extent from one another. In this regard, incases that an input path appears to be sufficiently similar to aresolved path, the resolved path can be transformed in a manner thatcorresponds with the input path. The transformed resolved path can thenbe generated as a path suggestion. By way of example only, assume aFréchet distance indicates an input path is sufficiently similar to aresolved path (e.g., as determined by the path analyzer 304). In such acase, a path suggestion of the resolved path transformed by the matrixtransformation M can be generated. Using the matrix M to transform theresolved path enables generation of a suggested path that correspondswith the input path. For instance, upon computing a Fréchet distance, itcan be determined that the input path is close to being a rotated,scaled, and/or translated version of a particular resolved path. Assuch, a path suggestion that is a rotated, scaled, and/or translatedversion of the resolved path can be generated such that instead ofresolving a freeform input path as input, the transformed version of theresolved path can replace the freeform input path.

Another beautification rule that can be applied to generate a pathsuggestion(s) for an input path is a transformation adjustment rule. Atransformation adjustment refers to a modification(s) being performed toa transformed path to create symmetries, align paths, and/or equalizespacing. In this regard, when two paths are similar to one another, atransformation adjustment can be applied to improve the preciseness of apath (e.g., an input path). As such, for an input path and a resolvedpath of the same shape, a transformation adjustment can be performed toprovide a path suggestion for the input path. For example, assume thatone path is determined to be 1.1 times the size of another path. Beingexactly the same size, however, may be more precise and, accordingly,provided as a path suggestion.

To generate a path suggestion in the form of a transformationadjustment, in instances that an input path is similar to a resolvedpath, a transformed path that generally aligns with an input path (byway of rotation, scale, and/or translation of a resolved path) isadjusted. As such, to determine a path suggestion(s) based ontransformation adjustments, a matrix M that transforms a resolved pathto correspond, or align, with an input path, can be separated intorotation, scale, and translation components as follows:rotation=atan 2(s sin,s cos)scale=/√{square root over (s cos² +s sin²)}translation=(tx,tx)

A transformation, or matrix transformation, can be adjusted in variousways to generate any number of suggestions, for instance, using therotation component, the scale component and/or the translationcomponent. As is described, various adjustments may include rotationsnapping, scale snapping, translation snapping, step-transform snapping,and/or reflection-axis snapping.

Rotation snapping refers to a rotation adjustment to a transformation(transformation of a resolved path) to generate a path suggestion. Todetermine a rotation adjustment to apply, the rotation componentassociated with the transformation of a resolved path can be used. Insome embodiments, if the rotation component is close to or about anangle that is an integral divisor of 2π, an adjusted transformation canbe applied accordingly so that a path suggestion is provided with thatprecise angle (e.g., 45 degrees). For example, assume that the rotationcomponent associated with a path transformation is 43 degrees. Because43 degrees is about 45 degrees, an integral divisor of 2π, the pathtransformation can be adjusted to 45 degrees to provide a pathsuggestion that has an angle of 45 degrees. Such a path suggestion canbe beneficial to the user as the user may have intended to provide afreeform input with a 45 degree angle. FIG. 6 provides an example resultof rotation snapping. In FIG. 6, drawing 602 represents freeform inputsprovided by a user, while drawing 604 represents transformationadjustments applied to the freeform input to obtain a symmetricaloutput. One example of rotation snapping is applied in association withpaths 606. Any threshold value can be used to determine whether therotation component is sufficiently close to a target rotation (e.g.,integral divisor of 2π). Further, although an integral divisor of 2π isused herein as a target rotation for assessing and performing rotationsnapping, as can be appreciated, any rotations can be designated.

Scale snapping refers to a scale adjustment to a transformation(transformation of a resolved path) to generate a path suggestion. Todetermine a scale adjustment to apply, the scale component associatedwith the transformation of a resolved path can be used. In someembodiments, if the scale component is close to or about an integer orhalf an integer, an adjusted transformation can be applied accordinglyso that a path suggestion is provided with that precise scale (e.g.,multiple of integer or half integer). For example, assume that the scalecomponent associated with a path transformation is 1.9. Because a scaleof 1.9 is close to the integer 2, the path transformation can beadjusted to a scale of 2 to provide a path suggestion having a scale of2. Such a path suggestion can be beneficial to the user as the user mayhave intended to provide a freeform input that is twice the scale of anexisting path. Any threshold value can be used to determine whether thescale component is sufficiently close to a target scale (e.g., integeror half integer). Further, although an integer and half integer are usedherein as a target scale for assessing and performing scale snapping, ascan be appreciated, any scales can be designated (e.g., quarterintegers, etc.).

Translation snapping refers to a translation adjustment to atransformation (transformation of a resolved path) to generate a pathsuggestion. To determine a translation adjustment to apply, acomponent(s) associated with the transformation of a resolved path canbe used. In some embodiments, translation snapping can take severalforms. As one example, if the transformation includes a rotationcomponent, a rotation center is identified and compared to existingpoints in the drawing. If the rotation center is sufficiently close toan existing point, the translation is adjusted to place the center ofrotation at that point. As another example, if the transformed path is areflected version of a resolved path, the axis of reflection is computedand, thereafter, the resolved path is reflected across this axis. If thepath is sufficiently close to this reflected path, we adjust thetranslation to move it to that position. As yet another example, the xand/or y components of the translation can be adjusted to zero (or othertarget value, such as a half integer). For instance, assume that thetranslation component associated with a transformed path is (100, 3). Insuch a case, the user may have desired to translate a curved path inputby 100 in the lateral direction, but have the same y-coordinate suchthat two paths are aligned. Accordingly, the translation can be adjustedto (100, 0). Such a path suggestion can be beneficial to the user as theuser may have intended to provide a freeform input that represents aparticular translation. Any manner or number of rules can be applied todetermine translation adjustments for generating path suggestions.

Step-transform snapping enables creation of multiple, equallytransformed copies of a path. For example, FIG. 6 provides an example ofstep-transform snapping in relation to paths 608. Generally, to performstep-transform snapping, a first transformation associated with tworesolved paths is compared to a second transformation between a resolvedpath and an input path. When the first transformation between theresolved paths is determined to be sufficiently similar to the secondtransformation between one of the resolved paths and the input path, thesecond transformation can be adjusted to be the same as the firsttransformation to create equally transformed copies of a path.

By way of example, and with reference to FIGS. 7A and 7B, a new inputpath T 702 is compared to three existing paths R 704, C 706 and D 708.Assume that the transformation matrix M_(DT) from path D to path T issimilar to the transformation matrix M_(CD) from path C to path D. Assuch, the step transformation between path D and T can be adjusted toequal the step transformation between path C and D so that path T ispositioned to match the step transform between paths C and D, asillustrated in FIG. 7B. Path T 710 as reflected in FIG. 7B can then beprovided as a suggested path. In some cases, matrices relative to path Rmay be stored, while other matrices are not stored. In such cases,matrix M_(RC) and M_(RD) can be used to compute M_(CD). Accordingly,when matrix M_(DT) is to be the same as M_(CD), this can be performed byadjusting M_(RT) so that it results in M_(DT) being the same as M_(CD).Although this example only includes translation in the step transform,other transformations including rotation, scale, and/or reflection arecontemplated to perform step-transform snapping.

Reflection-axis snapping is used to reflect paths against an axis ofreflection or to reflect a path across an existing line segment. Forexample, FIG. 6 provides an example of a reflection axis 610 for use inreflection-axis snapping. To perform reflection-axis snapping, existingaxes of reflection and line segments can be identified. An existing axisof reflection may exist when one existing path is a reflected version ofanother existing path. As such, the existing axis can be used as apotential reflection axis for additional paths (e.g., a new input path).If a new input path appears reflected, its axis of reflection can becompared to existing axes. When the axis of reflection associated withthe new input path is sufficiently close to an existing axis, asuggestion to reflect across the existing axis can be generated.

Another beautification rule that can be applied to generate a pathsuggestion(s) for an input path is an arc and circle center snappingrule. An arc and circle center snapping rule is generally used to aligna center point of an arc or circle with a point of a resolved path. Forexample, a center point of an arc or circle might be aligned with anendpoint of another path, a center associated with another arc or circlepath, a center of rotation associated with another path, a center of apolygon associated with a resolved path (e.g., polygons composed fromseries of line segments), etc. To align a center point of an arc orcircle with a resolved path point, the distance between an input centerand potential resolved path points can be evaluated. When the inputcenter point is within a threshold distance of a resolved path point,the input center point might be automatically snapped or aligned withthe resolved path point and the radius of the input arc or circle mightbe adjusted. In another case, when the input center point is within athreshold distance of a resolved path point(s), a suggestion to snap oralign the input center point with the resolved path point may beprovided to a user.

In some implementations, a predetermined threshold distance may beapplied to determine if the input center point is within a thresholddistance of a resolved path point. For instance, a standard searchdistance radius D may be assessed to determine if the input center pointis within the distance radius D relative to a resolved path point. Inanother implementation, a threshold distance can be dynamicallydetermined and used to determine if the input center point is within thedynamically determined threshold distance. Such an adaptive searchradius can be beneficial to effectively capture a user's intent. Forexample, arcs with small angular spans are difficult to draw preciselywithout a guide (e.g., users tend to draw the arc too curved). As such,the identified center of the input arc might be positioned at a distancetoo far apart from a desired center point. In the event a fixedthreshold distance D is used to assess whether the center of the inputarc is within the distance D of a resolved path point, the center of theinput arc might not be aligned with a desired resolved path point. As aresult, adaptive expansion of the search radius D′ increases thelikelihood that an imprecise input will provide the user the expected,precise output.

For example, and with reference to FIGS. 8A-8C, assume that a resolvedpath 802 of FIG. 8A exists and has a resolved center point 804. Furtherassume that input path 806 is drawn by a user. Using a fixed threshold D808, it can be determined that the center point 810 of the input path isnot within threshold distance D to the resolved center point, asillustrated in FIG. 8B. As such, the center point 810 is not aligned orsnapped to the resolved center point 804. Using an adaptive searchradius D′ 812 of FIG. 8C, however, it can be determined that the centerpoint 810 of the input path is within the threshold distance D′ to theresolved center point. Accordingly, the center point 810 is aligned orsnapped to the resolved center point 804. In addition, the radius of arc806 is adjusted to be the distance between arc 806 and the resolvedcenter point 804.

Various methods may be employed to adaptively modify a thresholddistance for assessing whether to align an input center point with aresolved path point. In some cases, an adaptive threshold might bedetermined such that the search radius or threshold distance becomeslarger as the span of the arc (e.g., θ) becomes smaller. As one example,the adaptive threshold D′ can be determined as follows:2r(1−θ/2π)  Equation 3wherein θ is the span of the input arc, and r is its radius. θ/2π refersto a fraction of a circle. As such, if θ equals π, θ/2π is ½ a circle.As can be appreciated, 1−θ/2π approaches 1 as the arc gets smaller.

In some cases, the adaptive threshold might be a selection between D′ orD. For example, a maximum distance of D or an adaptive distance D′(e.g., 2r(1−θ/2π) might be selected for use in assessing distancebetween an input center path and a resolved path point, as shown below:

$\begin{matrix}{{Distance} = {\max( {D,{2{r( {1 - \frac{\theta}{2\pi}} )}}} )}} & {{Equation}\mspace{14mu} 4}\end{matrix}$wherein θ is the span of the input arc, r is its radius, and D is thestandard or predetermined search distance radius. In one implementation,a value for D of 30 view space pixels is used.

As previously described, other beautification rules can be applied togenerate a path suggestion(s) for an input path. For example, otherbeautification rules may include line detection, arc detection, endpointsnapping, end tangent alignment, line parallelism and perpendicularity,line length equality, and path offset, etc. For the line detection rule,line straightness is estimated by measuring a ratio between length of apath and a distance between its endpoints. For the arc detection rule,an input path is sampled and a least-squares circle fit is performed onthe samples to obtain center and radius parameter values. To determinethe angular span value, the samples are projected onto the circle fit.The arc can then be sampled again and the discrete Fréchet distanceevaluated between the arc samples and the samples of the input path.When the span is close to 2π or the path is closed, it is replaced witha full circle.

For the endpoint snapping rule, a distance between each of the pathendpoints and resolved endpoints is examined. Additionally, snapping toinner parts of the resolved paths is also examined. Specialized testsbased on the properties of line segments and circular arcs lower thecomputational complexity of this operation. For the end tangentalignment rule, if the path endpoint is snapped, the angle between itstangent and the tangent of the point to which it is attached ismeasured. If the tangents are sufficiently close, the path is adjustedto make the attachment smooth.

For the line parallelism and perpendicularity rule, the angle betweentwo line segment paths is compared with the angle needed to satisfy theparallelism or perpendicularity constraint. The distance taken betweenthe line segments is also taken into account to slightly increase thepriority of nearby paths. For line length equality, the ratio of lengthof both tested line segments is evaluated. The mutual distance isincorporated into a final likelihood computation. For the path offsetrule, offset paths generalize line parallelism. To detect these paths,the beautification assistant module 108 progresses along the path andmeasures its distance to the resolved path.

In accordance with embodiments of the present invention, the pathsuggestion generator 306 can generate path suggestions based onsingle-segment path processing and/or multi-segment path processing.Single-segment path processing refers to processing a path (e.g., inputpath) based on a single segment. In some cases, a single segment is asegment without any corners detected in the segment. In other cases, asingle segment can be processed irrespective of having detected corners.For instance, an entire path with multiple segments, defined or split bycorner features, can be processed as a single segment to provide a pathsuggestion(s). Single-segment path processing can utilize any number ofthe beautification rules described above with respect to asingle-segment path to generate a path suggestion(s).

Multi-segment path processing refers to processing a path (e.g., inputpath) based on a multiple segments. In some cases, multiple segments canbe detected based on corner detection, as described above. In thisregard, segments defined or split by corner features of an input pathcan be individually processed to provide suggestion paths. By way ofexample, assume that a single input stroke is drawn generally in theshape of a triangle. For instance, a user may draw a triangle by way oftouch input without lifting her or his finger from the touch screenuntil the triangle is completed, or mostly completed. In such a case,corners of the triangle can be detected to generate multiple segmentsfor processing or evaluating. As such, once divided into segments, thepath suggestion generator 306 can utilize the segments along with one ormore beautification rules to generate path suggestions for the inputpath. To this end, the path suggestion generator 306 provides pathsuggestions based on multiple segments of a single stroke (e.g., inputpath). Such an implementation can provide more accurate path suggestionsas opposed to requiring a user to draw every segment independently(e.g., draw a 1^(st) stroke, draw a 2^(nd) stroke, and draw a 3^(rd)stroke to complete a triangle).

As described, multi-segment path processing enables processing of pathswith multiple segments. For example, assume that one input path is drawnby a user and, upon detecting a corner (e.g., via path analyzer 304),the path suggestion generator 306 can process the multiple segmentsusing one or more beautification rules. In some implementations,segments of the path, such as an input path, can be processed one at atime to generate one or more path suggestions to provide as output. Forexample, a first segment can be assessed to determine a first set ofpath suggestions; a second segment can then be assessed to determine asecond set of path suggestions, and so on. The second set of pathsuggestions might be in addition to the first set of path suggestions.In other cases, the second set of path suggestions modify the first setof path suggestions based on the assessment of the second segment. Forinstance, processing multi-segment input may include automatic selectionof intermediate path suggestions.

As the number of potential path suggestions can increase significantlyas multiple segments are analyzed, in some implementations, the pathsuggestions can be reduced to make the evaluation of complex inputscomputationally feasible within real-time-to-interactive response time.To reduce the number of path suggestions, a threshold number of uniquesuggestions can be applied. For instance, in some cases, after analyzingeach of the segments, the total number of path suggestions may belimited (e.g., 10 path suggestions). In other cases, the number ofunique suggestions for each segment can be limited (e.g., 3 pathsuggestions for each segment or segment addition). Alternatively oradditionally, the individual segments can be processed in abreadth-first manner that enables reduction once all the parallel statesreach the same depth (i.e., all have the same number of processedsegments). Each intermediate state can be assigned a value that iscalculated as the arithmetic mean of the scores of the processedsegments. N_(IS) intermediate states can be further analyzed while theremaining intermediate states are discarded. The performance ofmulti-segment path processing may be determined by the number ofsegments K and the intermediate stack size N_(IS), with N_(IS)=1 beingperformance-wise equal to sequential processing of individual segments.

As can be appreciated, as the individual segments are associated with asingle path (e.g., an input curve), the beautified proposed segments canbe consecutively joined to constrain the position of the first end pointof each segment after the first segment. Additionally, if themulti-segment path is closed, the last segment's final endpoint can beconstrained, which can decrease ambiguity.

By way of example only, and with reference to FIG. 9, assume that cornerdetection (e.g., applied via path analyzer 304) detects three cornersand splits the input path 902 into three segments, segment 904, 906, and908, which may be processed sequentially. Initially, the first segment904 is assessed to determine one or more path suggestions (e.g., usingany number of beatification rules). As shown in FIG. 9, path suggestions910 (an arc) and 912 (straight line) are generated. Turning to thesecond segment 906, path suggestions 914, 916, 918, and 920 can begenerated, for instance, based on the previous segments and, in somecases, a resolved path(s). As shown in FIG. 9, the beginning point ofthe second segment 906 may be constrained to align with or match thefinal endpoint of the previous segment 904. Further, assume that alimited number of three path suggestions is desired in connection witheach segment. In such a case, the fourth path suggestion 920 can beremoved as a path suggestion. Now, turning to the third segment 908,path suggestions 922, 924, and 926 are generated, for instance, based onthe previous segments and, in some cases, a resolved path(s).

The path provider 308 is generally configured to provide a set of one ormore path suggestions. As illustrated in FIG. 3, the path provider 308can provide a suggested path 316 and a suggested path 318. Although notillustrated, the suggested paths can be provided for display on the userdevice. In a client-server environment, such suggested paths can beprovided over a network to a user device for display on the user device.As previously described, a path suggestion refers to a suggestion orrecommendation of a path that can replace or modify another path, suchas an input path. In some cases, a path suggestion(s) can be provided asan alternative or option for an input path that is presented to a userfor selection. Upon the user selecting a particular path suggestion, acorresponding path, such as an input path, can be replaced or modifiedto replicate the selected path suggestion. In other cases, a pathsuggestion(s) may be automatically implemented to modify or replace aninput path. For example, an input path may be automatically convertedfrom one curved line to another curved line without selection from auser. As can be appreciated, in such cases, the user may have the optionto undo the automatic implementation.

The presentation of path suggestions can occur in any manner. In somecases, multiple path suggestions are simultaneously presented. In othercases, path suggestions are subsequently presented such that only onesuggestion is presented at a time. In such a case, a user may switchamong path suggestions, for example, using a tool panel. The first pathsuggestion may be a suggestion associated with a greatest or highestpath score, while a last suggestion may be the original input path. Auser may select a currently presented suggestion in any manner, such asby drawing a new input path or changing a selection. In some cases, toprovide assistance to a user, a simple visualization of appliedbeautification rule(s) can be provided along with the suggested path.Such a visualization can provide feedback to the user about imposedconstraints and relations of the user input. For example, with referenceto FIGS. 10A-10C, FIGS. 10A-10C illustrate visual annotations inaccordance with embodiments herein. In particular, FIG. 10A illustratesa visual annotation indicating a line perpendicularity and endpointsnapping rule, FIG. 10B illustrates a visual annotation indicating aline parallelism and single coordinate snapping rule, and FIG. 10Cillustrates a visual annotation indicating a path transformation rule.

In some cases, the path provider 308 can select one or more pathsuggestions to provide based on a corresponding path score for pathsuggestions. Such a score can be generated or determined by anycomponent, such as the path suggestion generator 306 (e.g., inassociation with a beautification rule(s)), the path provider 308, oranother component. A path score can represent a likelihood that asuggested path is correct or intended by a user. For example, asame-line-length rule might, for input that is a line segment, createpath suggestions that are the same lengths as existing line segments,along with scores that indicate how close the segment's initial lengthis to the modified length of the corresponding path suggestion. As such,in some cases, the scores may reflect an amount of adjustment performedby respective rules to achieve a respective path suggestion. In somecases, each rule may include a threshold that determines that the scorefor a path suggestion is too low and, in that case, does not output asuggested path.

The path scores can be compared to one another and/or to a thresholdscore to determine which path suggestions to provide to a user. Forexample, for a particular beautification rule, path scores associatedwith path suggestions derived from the particular beautification rulecan be compared to one another to select one or more path suggestions toprovide to a user. As another example, path scores associated with pathsuggestions derived from various beautification rules can be compared toone another to select one or more path suggestions to provide to a user.

Path scores can be determined in any number of ways and may varydepending on the particular beautification rule being applied. In somecases, multiple prior instances of an aspect may strengthen thelikelihood a user intended a particular path. For example, with respectto a transformed path, if the drawing includes multiple instances of apath, it is more likely that the user intended a new input path to matchthe previously resolved paths. As such, a score for a suggestedtransformed path may be boosted by replacing or modifying the score with1−(1−s)^(1n i), where i is the number of existing instances. As anotherexample, with respect to reflection axis snapping, for an axis that hasbeen used multiple times for path reflection, it is more likely that theuser intended a new input path to be reflected via that axis. According,a score for a suggested transformation adjustment may be increased byreplacing or modifying the score with 1−(1−s)^(1n i), where i is thenumber of instances the axis has been used.

Referring now to FIG. 11, a flow diagram is provided showing anembodiment of a method 1100 for facilitating beautification of freeformdrawings. In particular, FIG. 11 provides a method for implementing anarc and circle center snapping beautification rule. Each block of method1100 and other methods described herein comprises a computing processthat may be performed using any combination of hardware, firmware,and/or software. For instance, various functions may be carried out by aprocessor executing instructions stored in memory. The methods may alsobe embodied as computer-usable instructions stored on computer storagemedia. The methods may be provided by a standalone application, aservice or hosted service (standalone or in combination with anotherhosted service), or a plug-in to another product, to name a few.

Initially, at block 1102, an arc input path is obtained. An arc inputpath can be provided by a user, for example via a touch screen, andobtained by a beautification assistant component (e.g., beautificationassistant component 302 of FIG. 3). At block 1104, a resolved path pointis identified. A resolved path point refers to a point on or associatedwith a resolved path, such as an endpoint of another path, a centerassociated with another arc or circle path, a center of rotationassociated with another path, a center of a polygon associated with aresolved path (e.g., polygons composed from series of line segments),etc. At block 1106, a center point of the arc input path is determined.At block 1108, an adaptive radius distance is determined in associationwith the center point of the arc input path. In embodiments, theadaptive radius distance can be determined such that the search radiusbecomes larger as the span of the arc (e.g., θ) becomes smaller.Subsequently, at block 1110, it is determined whether the adaptiveradius distance is greater than a predetermined radius distance. If theadaptive radius distance is greater than the predetermined radiusdistance, the adaptive radius is used to determine if a center point ofthe arc input path is within the adaptive radius distance from theresolved path point, as indicated at block 1112. If so, a pathsuggestion is provided that aligns the center point of the arc inputpath with the resolved path point and adjusts the radius to be thedistance between the arc input path and the resolved path point, asindicated at block 1114. If not, the method ends, as indicated at block1116. Returning to block 1110, if the adaptive radius distance is notgreater than the predetermined radius distance, the predetermined radiusdistance is used to determine if a center point of the arc input path iswithin the predetermined radius distance from the resolved path point.This is indicated at block 1118. If so, a path suggestion is providedthat aligns the center point of the arc input path with the resolvedpath point and adjusts the radius to be the distance between the arcinput path and the resolved path point, as indicated at block 1114. Ifnot, the method ends, as indicated at block 1116.

Referring now to FIG. 12, a flow diagram is provided showing oneembodiment of a method 1200 for facilitating beautification of freeformdrawings. In particular, FIG. 12 provides a method for implementing apath transformation beautification rule. Initially, at block 1202, acurved input path is obtained. A curved input path can be provided by auser, for example via a touch screen, and obtained by a beautificationassistant component (e.g., beautification assistant component 302 ofFIG. 3). At block 1204, a transformation that aligns a resolved pathwith the curved input path is identified. In embodiments, to alignpaths, an affine similarity matrix that transforms the resolved path tomatch the input path as closely as possible can be determined. An affinesimilarity matrix can include a composition of a rotation, a scale, anda translation. At block 1206, the transformation that aligns theresolved path with the curved input path is used to determine an extentof similarity between the resolved path and the curved input path. Forexample, the resolved path can be multiplied by an affine similaritymatrix. Thereafter, a Fréchet distance can be used to determine anextent of similarity between the resolved path and the curved inputpath.

At block 1208, a determination is made as to whether the similaritybetween the resolved path and the curved input path exceeds a similaritythreshold. In such a case, it might be determined if a similaritymeasure is greater than a predetermined similarity threshold or if asimilarity measure is greater than other similarity measures associatedwith other input-resolved path pairs. If it is determined that thesimilarity between the resolved path and the curved input path does notexceed a similarity threshold, the method ends, as indicated at block1210. On the other hand, if it is determined that the similarity betweenthe resolved path and the curved input path does exceed a similaritythreshold, a suggested path is generated in the form of the resolvedpath transformed by the identified transformation that aligns a resolvedpath with the curved input path. This is shown at block 1212. At block1214, the suggested path is provided as a path suggestion to the uservia a user device.

Referring now to FIG. 13, a flow diagram is provided showing oneembodiment of a method 1300 for facilitating beautification of freeformdrawings. In particular, FIG. 13 provides a method for implementing atransformation adjustment beautification rule. Initially, at block 1302,a determination is made that an input curved path is sufficientlysimilar to a transformed resolved path. A transformed resolved pathrefers to a resolved path that, when transformed, generally aligns withan input path (by way of rotation, scale, and/or translation of aresolved path). To determine an input path is sufficient similar to atransformed resolved path, a Fréchet distance may be computed as asimilarity measure between the paths. At block 1304, a transformationapplied to the resolved path is separated into components, such asrotation, scale and translation components. At block 1306, eachcomponent is analyzed to determine whether the particular component isto be adjusted to result in a more precise transformation. For instance,a rotation component may be assessed to identify whether the rotation isnear or about a predetermined amount of rotation (e.g., an integraldivisor of 2π). As another example, a scale component may be assessed toidentify whether the scale is near or about a predetermined scale amount(e.g., an integer of half integer). As yet another example, atranslation component may be assessed to identify whether thetranslation is near or about a predetermined translation amount (e.g., atranslation of 0). If one or more components are to be adjusted toresult in a more precise transformation, the component(s) is adjusted togenerate an adjusted transformation to be applied, as indicated at block1308. Otherwise, the method ends at block 1310. At block 1312, asuggested path is generated in the form of the resolved path transformedby the identified adjusted transformation. At block 1314, the suggestedpath is provided as a path suggestion to the user via a user device.

With reference to FIG. 14, a flow diagram is provided showing oneembodiment of a method 1400 for facilitating beautification of freeformdrawings. In particular, FIG. 14 provides a method for applyingbeautification techniques to a path having multiple segments. Initially,at block 1402, a curved input path is obtained. A curved input path canbe provided by a user, for example via a touch screen, and obtained by abeautification assistant component (e.g., beautification assistantcomponent 302 of FIG. 3). At block 1404, one or more corners of thecurved input path are detected. A corner can be detected in any numberof ways. In one embodiment, a corner can be detected by calculatingtangent vectors at sample points along curves. At block 1406, the curvedinput path is separated into segments based on the detected one or morecorners. At block 1408, for each segment, one or more path suggestionsare generated using one or more beautification rules. In someimplementations, segments of the input path can be processed one at atime to generate one or more path suggestions to provide as output. Forexample, a first segment can be assessed to determine a first set ofpath suggestions; a second segment can then be assessed to determine asecond set of path suggestions, and so on. The second set of pathsuggestions might be in addition to the first set of path suggestions.In other cases, the second set of path suggestions modify the first setof path suggestions based on the assessment of the second segment. Atblock 1410, at least one of the one or more path suggestions areselected for providing to the user. Path suggestions may be selectedbased on scores associated with each potential path, etc.

Turning now to FIG. 15, FIG. 15 provides a diagram of an exemplarycomputing environment suitable for use in implementation of the presentdisclosure. Computing device 1500 includes bus 1510 that directly orindirectly couples the following devices: memory 1512, one or moreprocessors 1514, one or more presentation components 1516, input/output(I/O) ports 1518, input/output components 1520, and illustrative powersupply 1522. Bus 1510 represents what may be one or more busses (such asan address bus, data bus, or combination thereof). Although the variousblocks of FIG. 15 are shown with lines for the sake of clarity, inreality, delineating various components is not so clear, andmetaphorically, the lines would more accurately be grey and fuzzy. Forexample, one may consider a presentation component such as a displaydevice to be an I/O component. Also, processors have memory. Theinventors recognize that such is the nature of the art and reiteratethat the diagram of FIG. 15 is merely illustrative of an exemplarycomputing device that can be used in connection with one or moreembodiments of the present invention. Distinction is not made betweensuch categories as “workstation,” “server,” “laptop,” “handheld device,”etc., as all are contemplated within the scope of FIG. 15 and referenceto “computing device.”

Computing device 1500 typically includes a variety of computer-readablemedia. Computer-readable media can be any available media that can beaccessed by computing device 1500 and includes both volatile andnonvolatile media, removable and non-removable media. By way of example,and not limitation, computer-readable media may comprise computerstorage media and communication media. Computer storage media includesboth volatile and nonvolatile, removable and non-removable mediaimplemented in any method or technology for storage of information suchas computer-readable instructions, data structures, program modules, orother data. Computer storage media includes but is not limited to, RAM,ROM, EEPROM, flash memory or other memory technology, CD-ROM, digitalversatile disks (DVDs) or other optical disk storage, magneticcassettes, magnetic tape, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to store thedesired information and which can be accessed by computing device 1500.Computer storage media does not comprise signals per se. Communicationmedia typically embodies computer-readable instructions, datastructures, program modules, or other data in a modulated data signalsuch as a carrier wave or other transport mechanism and includes anyinformation delivery media. The term “modulated data signal” means asignal that has one or more of its characteristics set or changed insuch a manner as to encode information in the signal. By way of example,and not limitation, communication media includes wired media such as awired network or direct-wired connection, and wireless media such asacoustic, RF, infrared, and other wireless media. Combinations of any ofthe above should also be included within the scope of computer-readablemedia.

Memory 1512 includes computer-storage media in the form of volatileand/or nonvolatile memory. The memory may be removable, non-removable,or a combination thereof. Exemplary hardware devices include solid-statememory, hard drives, optical-disc drives, etc. Computing device 1500includes one or more processors that read data from various entitiessuch as memory 1512 or I/O components 1520. Presentation component(s)1516 present data indications to a user or other device. Exemplarypresentation components include a display device, speaker, printingcomponent, vibrating component, etc.

I/O ports 1518 allow computing device 1500 to be logically coupled toother devices including I/O components 1520, some of which may be builtin. Illustrative components include a microphone, joystick, game pad,satellite dish, scanner, printer, wireless device, etc. The I/Ocomponents 1520 may provide a natural user interface (NUI) thatprocesses air gestures, voice, or other physiological inputs generatedby a user. In some instances, inputs may be transmitted to anappropriate network element for further processing. An NUI may implementany combination of speech recognition, touch and stylus recognition,facial recognition, biometric recognition, gesture recognition both onscreen and adjacent to the screen, air gestures, head and eye tracking,and touch recognition associated with displays on the computing device1500. The computing device 1500 may be equipped with depth cameras, suchas stereoscopic camera systems, infrared camera systems, RGB camerasystems, and combinations of these, for gesture detection andrecognition. Additionally, the computing device 1500 may be equippedwith accelerometers or gyroscopes that enable detection of motion. Theoutput of the accelerometers or gyroscopes may be provided to thedisplay of the computing device 1500 to render immersive augmentedreality or virtual reality.

The present invention has been described in relation to particularembodiments, which are intended in all respects to be illustrativerather than restrictive. Alternative embodiments will become apparent tothose of ordinary skill in the art to which the present inventionpertains without departing from its scope.

What is claimed is:
 1. A computer-implemented method, the methodcomprising: identifying a center point of an arc freeform path added toan electronic drawing, the arc freeform path added subsequently to aresolved path in the electronic drawing; determining that a point of theresolved path is within a threshold distance of the center point, thethreshold distance determined based on a span of the arc freeform path;and generating, based on determining that the point is within thethreshold distance, a path suggestion comprising an adjustment to thearc freeform path that aligns the center point of the arc freeform pathwith the point of the resolved path.
 2. The computer-implemented methodof claim 1, wherein the threshold distance is adaptive based on the arcfreeform path.
 3. The computer-implemented method of claim 1, whereinthe threshold distance is expandable based on the span of the arcfreeform path.
 4. The computer-implemented method of claim 1, whereinthe threshold distance is configured to decrease as the span of the arcfreeform path increases.
 5. The computer-implemented method of claim 1,further comprising determining the threshold distance as a greaterdistance selected from a predetermined distance or an adaptive distancebased on the arc freeform path.
 6. The computer-implemented method ofclaim 1, the adjustment to the arc freeform path further comprising anadjustment to radius and curvature of the arc freeform path.
 7. Thecomputer-implemented method of claim 1, further comprising identifyingthe center point of the arc freeform path by performing a least squarescircle fit on samples of the arc freeform path, and identifying thecenter point from the least squares circle fit.
 8. Thecomputer-implemented method of claim 1, further comprising identifyingthe span of the arc freeform path by: performing a circle fit on samplesof the arc freeform path; projecting the samples onto the circle fit;sampling the projected samples from the circle fit to identify projectedarc samples; and identifying the span based on a distance between theprojected arc samples and the samples of the arc freeform path.
 9. Thecomputer-implemented method of claim 1, the adjustment to the arcfreeform path further comprising replacing the arc freeform path with afull circle based on a determination that the span of the arc freeformpath is at least within a threshold of 2π.
 10. One or more computerstorage media storing a plurality of executable instructions, which,when executed by one or more processors, cause the one or moreprocessors to perform operations comprising: determining a thresholddistance from a center point of an arc input path, the thresholddistance being determined based on a span of the arc input path;determining that a point of a resolved path is within the thresholddistance from the center point of the arc input path; and based on thepoint of the resolved path being within the threshold distance from thecenter point of the arc input path, aligning the center point of the arcinput path with the point of the resolved path and adjusting a radiusassociated with the arc input path to be a distance between the arcinput path and the point of the resolved path.
 11. The one or morecomputer storage media of claim 10, wherein the threshold distance isconfigured to increase as the span of the arc input decreases.
 12. Theone or more computer storage media of claim 10, wherein the point of theresolved path comprises an endpoint of the resolved path, a centerassociated with the resolved path, or a center of rotation associatedwith the resolved path.
 13. The one or more computer storage media ofclaim 10, the operations further comprising determining the thresholddistance as a greater distance selected from a predetermined distance oran adaptive distance based on the arc input path.
 14. The one or morecomputer storage media of claim 10, the operations further comprisingidentifying an arc span of the arc input path by: performing a circlefit on samples of the arc input path; projecting the samples onto thecircle fit; sampling the projected samples from the circle fit toidentify projected arc samples; and identifying the arc span based on adistance between the projected arc samples and the samples of the arcinput path.
 15. A computer system comprising: one or more hardwareprocessors and memory configured to provide computer programinstructions to the one or more hardware processors; a freeform drawingcomponent configured to utilize the one or more hardware processors toreceive a freeform path drawn by a user as part of an electronicdrawing, the freeform path including an arc path, the electronic drawingincluding a resolved path that existed prior to receiving the freeformpath; a means for generating a path suggestion, utilizing the one ormore hardware processors, based on a determination that a point of theresolved path is within a search radius of a center point of the arcpath, the search radius determined as a greater distance selected from apredetermined distance or an adaptive distance based on the arc path;and a path provider configured to utilize the one or more hardwareprocessors to present the path suggestion to adjust the arc path. 16.The computer system of claim 15, wherein the means for generating a pathsuggestion is configured to adaptively expand the search radius based onthe arc path.
 17. The computer system of claim 15, wherein the means forgenerating a path suggestion is configured to adaptively expand thesearch radius as a span of the arc path becomes smaller.
 18. Thecomputer system of claim 15, wherein the path suggestion is configuredto adjust at least one of (i) a position of the arc path to align thecenter point of the arc path with the point of the resolved path, (ii)the radius of the input arc, or (iii) a curvature of the input arc. 19.The computer system of claim 15, wherein the path suggestion isconfigured to identify the center point of the arc path by performing aleast squares circle fit on samples of the freeform path, andidentifying the center point from the least squares circle fit.